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From Chaos to Order in a Ring of Coupled Oscillators with Frequency Mismatch

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Regularity and Stochasticity of Nonlinear Dynamical Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 21))

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In this chapter we describe the route to synchronization in a ring of three unidirectionally in the presence of a mismatch between their natural frequencies. Three coupled oscillators is a simplest network motif where each oscillator is nothing more than a node. Network motifs repeat themselves in a specific network or even among various networks, and can be responsible for particular functions. On the route to synchronization the oscillators pass through intermittent phase synchronization , phase synchronization , lag or anticipating synchronization with respect to the coupling strength and frequency mismatch. When the oscillators’ natural frequencies are very close to each other, they are chaotic for any coupling strength, whereas for larger mismatch and strong coupling they exhibit regular dynamics. The results of numerical simulations are in good agreement with electronic experiments.

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Pisarchik, A.N., García-Vellisca, M.A. (2018). From Chaos to Order in a Ring of Coupled Oscillators with Frequency Mismatch. In: Volchenkov, D., Leoncini, X. (eds) Regularity and Stochasticity of Nonlinear Dynamical Systems. Nonlinear Systems and Complexity, vol 21. Springer, Cham.

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